Are there any anthropological studies involving AI right now?
As far as I can tell (I've been doing searches here and there on and off since I saw this question a few hours ago) the closest we've gotten to 'simulations' on this is video-games, and to a degree movies, interestingly enough. I.e. entertainment media.

Games like Portal, System Shock (with the AI 'Shodan'), and others give interpretations of what AI systems could be capable of themselves. Mass Effect is more or less entirely based around existential concepts regarding extra-terrestrial, almost primordial AI beings that threaten the earth.

But there's even more to it than the whole 'evil robots taking over the world' aspect. There's the actual implementation of AI in video games, which is where much of this technology first makes contact with the general public.

We have facial-scanners that put you into NBA games, cities full of realistically reacting people (inFamous, Assassin's Creed), and games that learn how you play and adjust the game accordingly (Metal Gear Solid does some of that stuff, as well as being thematically AI-heavy). 

Ultimately, we only get things like the iPhone or VR headsets or other major proof-of-concept material only so often, but games are much more frequently implementing the most recent AI advances. 

Thus, even though many AI systems are being put into place in the general workforce (many Hospitals now turning to cloud and AI health services, as recent as this week), I don't think you can really go further than video games or movies for 'simulations' or extrapolations like the ones you seem to want. 

Analyzing the response to AI developments in games might be the closest thing currently possible. In terms of economic models or anything of that sort, I can find naught.